So this is the one thing I haven't tried...
I have done just about everything else suggested in this thread, save for swapping out hardware/trying things in a new system (both of which aren't possible for me).
After running through y'all's suggestions and a crapton of googling the symptoms, I've seen quite a few mentions of it potentially being a RAM issue. I have run Win7's Memtest, and it showed that everything was fine. However, I did find several folks online who noted it really was a RAM problem, even though the RAM passed the Memtest. They solved the issue by doing what joker did - lax the timings.
So how do I do that?